Decision Support Systems 52 (2012) 528–538

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Decision Support Systems

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Network optimization in supply chain: A KBGA approach

A. Prakash a, Felix T.S. Chan a,⁎, H. Liao b, S.G. Deshmukh c

a Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kongb College of Engineering, Industrial and Information Engineering, The University of Tennessee, USAc Department of Mechanical Engineering, Indian Institute of Technology, Hauz Khas, New Delhi-110016, India

⁎ Corresponding author at: Department of IndustrialHong Kong Polytechnic University, Hung Hom, Hong Ko

E-mail addresses: mfanuj@polyu.edu.hk (A. Prakash(F.T.S. Chan), deshmukh@mech.iitd.ernet.in (S.G. Deshm

0167-9236/$ – see front matter © 2011 Elsevier B.V. Alldoi:10.1016/j.dss.2011.10.024

a b s t r a c t

a r t i c l e i n f o

Article history:Received 28 February 2011Received in revised form 12 October 2011Accepted 23 October 2011Available online 26 October 2011

Keywords:Supply chainKnowledge ManagementGenetic AlgorithmKnowledge Based Genetic Algorithm

In this paper, we present a Knowledge Based Genetic Algorithm (KBGA) for the network optimization ofSupply Chain (SC). The proposed algorithm integrates the knowledge base for generating the initial popula-tion, selecting the individuals for reproduction and reproducing new individuals. From the literature, it hasbeen seen that simple genetic-algorithm-based heuristics for this problem lead to and large number of gen-erations. This paper extends the simple genetic algorithm (SGA) and proposes a new methodology to handlea complex variety of variables in a typical SC problem. To achieve this aim, three new genetic operators—knowledge based: initialization, selection, crossover, and mutation are introduced. The methodology devel-oped here helps to improve the performance of classical GA by obtaining the results in fewer generations.To show the efficacy of the algorithm, KBGA also tested on the numerical example which is taken from theliterature. It has also been tested on more complex problems.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

The current business environment is becoming increasingly un-certain, unpredictable, complex, and as a result, more and more com-petitive. Increased competition means that companies face the dualchallenge of cutting costs while being more responsive to the cus-tomers [1]. The researchers and practitioners throughout the worldrealize that though there may be diverse and situation specific solu-tions to the problems posed by these challenges, flexibility has to bethe essential feature of the tools to handle these changes. As compe-tition and complexity has increased, Supply Chain Management(SCM) has emerged as an increasingly important issue for companies.A supply chain links design, sourcing, manufacturing, and logistics ac-tivities across organizations. The chain links suppliers and customers,beginning with the production of rawmaterial by a supplier, and end-ing with the consumption of a product by the customer. In a supplychain, the flow of goods between a supplier and customer passesthrough several stages, and each stage may consist of many facilities[37]. In recent years, the supply chain network (SCN) design problemhas been gaining importance due to increasing competitiveness intro-duced by the market globalization [2,3,4]. The network design prob-lem is one of the most comprehensive strategic decision problemsthat need to be optimized for long-term efficient operation of wholesupply chain. It determines the number, location, capacity and type

and Systems Engineering, Theng.), mffchan@inet.polyu.edu.hkukh).

rights reserved.

of plants, warehouses, and distribution centers to be used. It alsoestablishes distribution channels, and the amount of materials anditems to consume, produce, and ship from suppliers to customers.Most of supply chain network design problems can be reduced tocapacitated facility location problem (CFLP) which is known to beNP-complete [16]; therefore, most of supply chain network designproblems are NP-hard [34,43].

In the present article, a new algorithm, KBGA, has been proposedand shows the application of it in the SCN optimization problem.The SCN problem is a very complex problem and the decision makingis also very difficult for the managers. In this study, two objectiveshave been considered, those are 1) minimization of the total averagecost per fill demand and 2) maximization of the demand fill rate. Bothof the objectives are conflicting in nature, therefore a pareto optimalfront has been achieved by applying KBGA. In the KBGA, the knowl-edge of the human being has been considered for the improvementof quality of solution. The knowledge base has helped in four stagesof the algorithm: initialization, selection, crossover, and mutation.With the help of knowledge base, all these steps provide the im-proved solution within very few generations. To show the efficacyof the proposed algorithm over Simple GA (SGA), a bench mark prob-lem from the literature has been taken and it is also tested on the fewmoderate size of the problems.

The remainder of this paper is described as following: Section 2presents the literature review of supply chain network optimizationand employment of genetic algorithm in it. Section 3 delineates thecomplexity of the problems whereas the mathematical model hasbeen described in Section 4. Section 5 describes the background ofSimple GA (SGA). The role of knowledge management has been

Supplier 1

Supplier 2

Supplier 3

Supplier 4

Central

Warehouse

L1-1

L1-2L1-3

L2-1

L2-2

L2-3

L3

L4

Retailers

Fig. 1. Potential suppliers and transportation modes.

529A. Prakash et al. / Decision Support Systems 52 (2012) 528–538

revealed in Section 6. The proposed algorithm knowledge based ge-netic algorithm (KBGA) has been discussed in Section 7 and the de-tailed procedure of KBGA has been portrayed in Section 8. Section 9illustrates the Numerical analysis of the given problem by using theproposed algorithm. In Section 10, the paper has been concludedwith some issues and future scope of the research.

2. Literature review

In literature, there are different studies dealing with the designproblem of supply networks and these studies have been surveyedby Erenguc et. al. [19], and Pontrandolfo and Okogbaa [35]. In tradi-tional SCM, the focus of the integration of SCN is usually on single ob-jective such as minimum cost or maximum profit [5,39,40]. Theseapproaches are involved in tackling the various components of costsor the tradeoffs between those components. Amiri [5] has presenteda lagrangian relaxation approach to minimize the total cost of twostage supply chain. Costa et al. [13] have worked on three stage sup-ply chain network optimization problem. The objective of the re-search is to minimize the total cost of supply chain. Recently, multiobjective optimization of SCNs has been considered by different re-searchers in literature [9,11,12]. Chan et.al. [10] developed a hybridapproach based on Genetic Algorithm (GA) and Analytic HierarchicalProcess (AHP) for production and distribution problems in multi-factory supply chain models. Guillen et al. [24] have worked onmulti-objective supply chain network designing problem. Theyemployed a branch and bound algorithm and the objectives are profitof supply chain and customer service. Whereas Altiparmak et al. [4]have considered total cost, customer service and capacity utilizationto design a supply chain network. Shen and Qi [38] proposed an inte-grated stochastic supply chain design model that takes into consider-ation the location, inventory and routing costs. They considered athree-tiered supply chain system consisting of one or more suppliers,distribution centers and customers with uncertain demand that fol-lows a certain probability distribution. Inventory holding costs andtransportation costs were assumed to exhibit economies of scale.Cardona-Valdes et al. [8] have presented a study of multi-echelonsupply chain network designing problem and they have consideredthe economical aspect with customer service level. Prakash and Desh-mukh [36] have also presented an approach to allocate the warehouseto the customers. They have also taken as a multi-criteria problem byconsidering transportation time and transportation cost.

Due to the complexity of the problem, various researchers areattracted towards the application of GA [6,17,21]. A hierarchical com-bination of mixed-integer programming and a genetic algorithm hasbeen proposed in Truong and Azadivar [44] to determine simulta-neously the values of quantitative as well as policy variables. Altipar-mak et al. [3] have also applied the GA to solve such problem withthree objectives: minimization of total cost, maximization of custom-er service, and maximization of capacity utilization. Farhani and Ela-hipana [20] have also applied GA for distribution networkoptimization. They considered two objectives: minimization of costsand minimization of the backorders. Gen et al., [22] have proposed aGA based approach to cope with network multiple objective prob-lems. Lee et al. [27] have also applied the GA for the optimization ofreverse logistics network problem.

From the aforementioned literature review, it has been seen thatthe researchers are concerned about the customer satisfaction i.e. tofulfill the demand within time and decrease the cost. Therefore,these two objectives are also considered in the present study. TheSCN optimization is a complex problem, so many researches areintended to application of GA in SCN problem but still it needs moreexploration. Most of the researchers have concentrated on theimprovement of the supply chain performance and very few haveconsidered the performance improvement of the algorithm concur-rently. Keeping in mind the same, the present study give an outlook

over both the objectives: performance improvement of supply chainand performance improvement of algorithm. If the improved algo-rithm will be applied, the quality of the solution will be better withinlesser time. The present paper proposes a new algorithm which hasthe inherent search capability of GA with the power of knowledgeand it is known as Knowledge Based Genetic Algorithm (KBGA).KBGA uses both the tacit and explicit knowledge.

3. Problem description

In supply chain network designing problem, logistic cost form themajor part of a supply chain's costs. Inventory control and distribu-tion planning, as fundamental logistical processes, affect the totalcosts of the supply chain to a great extent, but, on the other hand,have a great effect on the customers' demand fill rate. Every suppliershould deliver the right amount of goods, at the right time, and to theright place. The detailed problem has been described as following.

In the present research, a case study has been taken into the con-sideration to show the complexity of the network optimization prob-lem in supply chain. This problem is identical as considered by Ding etal. [18]. In this case there is a supply chain for “Classic” boots of anItalian textile company. The company outsourced production to out-side contractors and it focuses only on marketing issues. For the actu-al situation, the product is made by a unique supplier in Vietnam(Supplier 1). Boots are then collected in containers and transportedby boat from Hochimin harbor to Genova harbor. From Genoa, bootsare transported by trucks to the central warehouse near Ferrara,where they are stored. The product is then distributed to the retailersof the Italian market. The network is shown in Fig. 1 with the avail-able transportation links.

The main objective to solve such supply chain network optimiza-tion problem is to evaluate the selection of different suppliers or setof the suppliers and transportation links simultaneously, whereasthe performance criteria are the total cost and demand fill rate. Simul-taneously, this study also satisfies some other goals like the impact ofthe performance by demand variation and the impact of inventorypolicy changing. From the figure, supplier 1 is the actual or existingsupplier which is situated in Vietnam and one of the new or proposedsuppliers (supplier 2) is in the Far East whereas supplier 3 is in theEast Europe and the last one (supplier 4) is the local supplier i.e.that is situated in Italy itself. In this study, to evaluate the total cost,six different costs have been taken into consideration. These costsare the engagement cost, purchasing cost, transportation cost, inven-tory holding cost, ordering cost and penalty cost due to unfilled de-mand of the orders. The cost provided from all the suppliers andduties according to their physical situations are given in Table 1.From the table, it is clearly shown that supplier 2 provides the bootsat the lowest cost. The transportation features are provided inTable 2. Table 2 shows the transportation lead time and cost for

Table 1Parameters for suppliers.

Supplier ID Engagementcost

Priceper pair

Duties Supply lead-time(day)

Min. order size(pair)

1 0 12.0 10% 15.0 10002 100000 10.0 20% 20.0 10003 80000 14.0 0 10.0 5004 100000 16.0 0 8.0 500

530 A. Prakash et al. / Decision Support Systems 52 (2012) 528–538

each transportation link. From the table, it can be said that the trans-portation cost of supplier 4 is less than any other supplier, whereassupplier 2 has the more transportation cost. Supplier 3 and supplier4 are more responsive because they are closer to the central ware-house. Only one transportation mode, using trucks, is provided foreach of them. For both the suppliers, the supply lead-time is veryshort, but on the other hand, the price is much higher than that ofthe two suppliers from Far East.

The mathematical modeling of the abovementioned problem hasbeen delineated in the next section.

4. Mathematical modeling

In the present problem of supply chain network optimization, theobjective is to assign the suppliers and their transportation link insuch a manner which can fulfill the demand at optimum cost. Themathematical model including notations, parameters, and objectivefunctions with constraints is as follows:

4.1. Notations

i Supplier's index (1,2,3…..n)j Transportation links' index (1, 2, 3….m)k Number of dayso Number of orders

4.2. Parameters

CEng Total Engagement CostCInv Total Inventory CostCPur Total Purchasing CostCOrd Total Ordering CostCTrans Total Transportation Costd Mean of Daily demand quantityDTotal Total demand of itemsDLost Total Lost DemandPCL Total Penalty Cost on lost demandp penalty cost per itemeci engagement cost for ith supplierNpuri Number of items purchased from ith supplierUCi Unit purchasing cost (determined by ith supplier)

Table 2Parameters for transportation links.

ID Transport modes Transportation lead-time Unit cost

Distributiontype

Mean(day)

Std. dev.(day)

Per pair

L1–1 Boat+truck Normal 20 1 0.5L1–2 Boat+plane+truck Normal 8 0.8 2.0L1–3 Plane+truck Normal 5 0.5 4.0L2–1 Boat+truck Normal 25 2 0.5L2–2 Boat+plane+truck Normal 10 1 2.0L2–3 Plane+truck Normal 5 0.5 4.0L3 Truck Constant 4 0 1.0L4 Truck Constant 2 0 0.2

Nk Inventory of items per dayh Holding cost per item per daynoi Number of orders placed to ith supplieroc Ordering cost per orderTRij Number of transshipped items from jth transportation link

of ith suppliertcij Transportation cost per item from jth transportation link of

ith supplierORsup i

Order placed to ith supplierLBsup i

lower bound limit of order placed to ith supplier (minimumnumber of items ordered)

4.3. Objectives

The objectives are to minimize the total average cost per fill de-mand and maximize the demand fill rate. The mathematical formula-tion for both the objective function is given below

Min f 1 ¼CEng þ CPur þ COrd þ CTrans þ CInv þ PCL

� �DTotal−DLostð Þ ð1Þ

Max f 2 ¼ DTotal−DLostð ÞDTotal

: ð2Þ

To calculate the first objective, the individual cost can be calculat-ed as follows:

CEng ¼ ∑ieci�zi ∀i ð3Þ

CPur ¼ ∑iNpuri

�UCi ∀i ð4Þ

COrd ¼ ∑i∑onoi

�oc�yoi ∀o; i ð5Þ

CTrans ¼ ∑i∑jTRij

�tcij�xij ∀i; j ð6Þ

CInv ¼ ∑kNk

�h ∀k ð7Þ

PCL ¼ DLost�p ð8Þ

Which are subjected to:

∑iOR supi

≥DTotal ð9Þ

OR supi≥LB supi

∀i ð10Þ

OR supi¼ ∑

jTRij

�xij ∀j ð11Þ

∑i∑jTRij

�xij≥DTotal ∀i; j ð12Þ

xij ¼ 1 if jth tranportation link of ith supplier is activated0 otherwise

�ð13Þ

yoi ¼ 1 if oth order is placed to ith supplier0 otherwise

�ð14Þ

zi ¼ 1 if ith supplier is engaged0 otherwise

�ð15Þ

k; o; p;Nk; LB supi≥0: ð16Þ

Randomly generated initial population of

chromosomes

Selection

Evaluation of each chromosome

Crossover

Mutation

Is satisfying the termination criteria?

Near Optimal Results

Start

Stop

No

Yes

Genetic Operators

Fig. 2. Flowchart of Simple Genetic Algorithm (SGA).

531A. Prakash et al. / Decision Support Systems 52 (2012) 528–538

The first objective function (Eq. (1)) is to minimize the average ofall the incurred cost. The last cost component is the penalty costwhich will be incurred for failing to meet demand.

The second objective function (Eq. (2)) is to maximize the de-mand fill rate i. e. the lost demand should be minimize.

Eqs. (3) to (8) show the formulation of different costs like engage-ment cost, purchasing cost, ordering cost, transportation cost, and in-ventory cost. The novelty of this mathematical model is to penalize oneach lost demand. The penalty cost has been stated in mathematicalform in Eq. (8).

The constraints are given in Eqs. (9) to (16). Eq. (9) shows that theorder placed to the supplier should not be less than demand of thecustomers whereas Eq. (10) illustrates that the order placed to an in-dividual supplier should not be less than a minimum number of itemsor lower bound of the order. The total number of transshipped itemsfrom all the transportation links of a supplier should be equal to theorder placed to that supplier and it should be more than total demandof customers. These constraints have been modeled mathematicallyin Eqs. (11) and (12). Finally, constraints in Eqs. (13)–(15) enforcethe binary nature of the configuration decisions while Eq. (16) im-poses the non-negativity restriction of the decision variables corre-sponding to transshipment, orders etc.

5. Background of SGA

Simple GA is an ‘intelligent’ probabilistic search algorithm thatsimulates the process of evolution by taking a population of solutionsand applying genetic operators in each reproduction. Each solution inthe population is evaluated according to some fitness measure. Fittersolutions in the population are used for reproduction. New ‘off spring’solutions are generated and unfit solutions in the population arereplaced. The cycle of evaluation–selection–reproduction is contin-ued until a satisfactory solution is found [23,29]. Holland [25] first de-scribed a GA, which is commonly called the Classical GA (CGA). Theworking of the CGA can best be understood by the following steps,which are shown in Fig. 2.

Step 1 Generate the initial population. Determine the size of the pop-ulation and the maximum number of the generation.

Step 2 Calculate the fitness value of each member of the initialpopulation.

Step 3 Calculate the selection probability of each member of the ini-tial population using the ratio of fitness value of that initialpopulation to the summation of the fitness values of the indi-vidual solutions.

Step 4 Select a pair of members (parents) that can be used for repro-duction using selection probability.

Step 5 Apply the genetic operators such as crossover, mutation, andinversion to the parents. Replace the parents with the newoff-spring to form a new population. Check the size of thenew population. If it is equal to the initial population size,then go to step 6, otherwise go to step 4.

Step 6 If the current generation is equal to the maximum number ofthe generation then stop, else move to step 2.

After searching a large amount of the literature in the area of GAapplication in supply chain, it has been found that there is a need ofmore exploration of this are in the research. This research intendsto demonstrate the advantage of Knowledge Management in GA ap-plications in the area of the network optimization problem of supplychain that is known for its computational complexity.

6. Background of KM

As Francis Bacon, an English philosopher, said, “Knowledge ispower”. To learn new things, maintain valuable heritage, create corecompetences, and initiate new situations, the power of knowledge

is a very important resource for both individual and organizationsnow and in the future. According to Nonaka [31], Knowledge hasbeen defined as “justified true belief” that increases an organization'scapacity for effective action. It has two dimensions: explicit and tacitknowledge. Davenport and Prusak [15] define knowledge as a fluidmix of framed experience, values, contextual information, and expertinsight that provides a framework for evaluating and incorporatingnew experiences and information. They suggest that it originatesand is applied only in the mind of knower and holders of tacit knowl-edge in organizations. It is embodied in documents, repositories, or-ganizational routines, processes, practices and norms. To respond tocompetitive challenges, otherwise-independent firms have becomemore closely coupled than in the past, often working in parallel tocomplete assignments spanning traditional boundaries and function-al areas. KnowledgeManagement (KM) provides processes to capturea part of tactic knowledge through informal methods and pointersand fairly high percentage of explicit knowledge, reducing the lossof organizational knowledge [32].

“KM is the formalization of and access to experience, knowledgeand expertise that create new capabilities, enable superior perfor-mance, encourage innovation and enhance customer value” [7].According to Tiwana [41], Knowledge Management is the ability tocreate and retain greater value from core business competencies.Beckman [7] realizes that Knowledge Management is the systematic,explicit, and deliberate building, renewal, and application of knowl-edge to maximize an enterprise's knowledge-related effectivenessand returns from its knowledge assets. Whereas, Tiwana and Balasu-bramanyam [42] feel that Knowledge Management addresses busi-ness problems particular to business—whether it's creating anddelivering innovative products or services or managing and enhanc-ing relationship with existing and new customers, partners, and

532 A. Prakash et al. / Decision Support Systems 52 (2012) 528–538

suppliers, or administrating and improving work practices and pro-cesses. Nietok [30] examines that knowledge has a connotation of‘potential for action’ and is different from information in terms of itsmore immediate link with performance. It is linked to the valuesand experience of the user, and therefore takes many forms. Onemay have knowledge of certain facts. Meiller et al. [28] observedthat there are four components of a knowledge base system: learning,simulation, problem solving and evaluation. They have used it forhealthcare system. A KM strategy can help tear down traditionalcross functional boundaries. KM entails helping people share andput knowledge into action by creating access, context, infrastructure,and simultaneously reducing learning cycles [14,15,33].

In the present paper, the knowledge based tool is motivated by theideas proposed by Wadhwa and Saxena [45]. The creation of today'sknowledge base requires blending of knowledge from diverse disci-plinary and personal skills based on perspectives where creative co-operation is critical for innovation. An integrated framework of KMhas been shown in Fig. 2. It shows the conversion of information toknowledge and integration of knowledge base with knowledge utili-zation. To convert the information to knowledge, the process followsthe various activities as verification, acquiring the filtered informa-tion, classification and creation of the knowledge from this informa-tion. All the acquired knowledge is stored in the knowledge base.After accumulation, the knowledge has been distributed to theknowledge users by following the steps like adaptation, attraction,engaging the people and teaches them how to use this knowledge.The knowledge synergy based thinking showed in Fig. 3 can signifi-cantly benefit the KM guided manufacturing endeavors.

7. Proposed Knowledge Based Genetic Algorithm (KBGA)

Although GA is a global search technique, its practical usefulnessdepends on the initialization of the problem, crossover and mutationtechniques and selection scheme for the next generation. Therefore, anumber of techniques have been developed for handling all the aboveconstraints. In the network optimization problem of supply chain,various researchers have explore the application of GA to improvethe system performance but very few researchers have worked onthe improvement of supply chain performance as well as algorithmperformance.

Information providers

Verification & Filtration

Acquire

Systematize

Create Knowledge

Knowledge

Conversion to Knowledge

Fig. 3. An integrated framework

In the present paper, we have introduced a concept of improvingthe performance of GA by exercising the knowledge based system,which will develop a faster algorithm for better performance of thesystem. It will employ on the basis of both tacit and explicit knowl-edge. For a search stratagem, it is very essential that it should alsohandle the inherent characteristics and complexities of the environ-ment. By employing the knowledge of the environment like supplychain and the complexities, i.e. flexibilities, we can get the better re-sult within lesser time than SGA. As it works with the knowledgebase, it is identified as KBGA. The proposed algorithm works notonly for improving the performance measures of the system like tra-ditional GA but the performance of the algorithm (Fig. 4). To enhancethis idea, the knowledge based initialization, knowledge based cross-over, knowledge based mutation, and knowledge based selectionhave also been incorporating in the algorithm. The procedure of thealgorithm has been described in the next section.

8. Procedure of KBGA for Network Optimization Problem

As stated in the previous section, it is clear that the strong point ofKBGA over SGA is the knowledge based generation of the initial pop-ulation instead of random generation. It is followed by the knowledgebased selection (KBS), Knowledge based crossover (KBC), and Knowl-edge based mutation (KBM) to provide the wider search space withinlesser time. The full procedure of KBGA has been shown in Figs. 5–8.All the steps of the proposed algorithm (KBGA) are as follows:

8.1. Knowledge based initialization (KBI)

In the first step of the algorithm, an initial population set of the so-lutions has been generated on the basis of the knowledge based sys-tem. In this step, firstly the information related to the systemenvironment like (supply chain structure, types of transportationlinks etc.), suppliers (location, unit price, lead time, minimum ordersize etc.), transportation (mode, transportation lead time, cost etc.),demand, inventory policy has been collected and filtered.

After that the performance measures, on which the system con-centrates, and the requirements have been decided. After this deci-sion making, the existing network has been evaluated with somebest known alternatives on the basis of performance measures. This

Base

Adapt

Attract

Engage the people

Learn

Knowledge Users

Knowledge Utilization

of Knowledge Management.

Start

Generate Initial Populationbased on the knowledge

Evaluate eachchromosome

Knowledge basedSelection

Knowledge basedCrossover

Knowledge basedMutation

Is satisfying theTermination

Criteria

Near Optimal Result

Stop

Knowledge BaseSystem

(Selection scheme,

Crossover Scheme)

Information Providersfrom Shop Floor

No

Yes

Fig. 4. Flowchart of KBGA.

533A. Prakash et al. / Decision Support Systems 52 (2012) 528–538

depends on the knowledge of network manager, supply chain man-agers. The tacit and explicit types of knowledge will be used for thisevaluation. After evaluation all the practiced alternatives, the best al-ternative will be selected and it will be the first solution or the start-ing point of the algorithm. This will be collected in the knowledgebase. Therefore, the initial seed is already improved; the later gener-ation will give the better results within lesser generation or con-verged to the better results in lesser generations.

The knowledge base provides the initial population for the pro-posed algorithm. Thus, here all the constraints related to the systemor problem has been taken into the consideration. Hence, it can besaid that the seed of initial population will work better than randomlygenerated population. After getting the initial population, the evalua-tion process is started and it is described in the next section.

For initialization, various information is needed and on the basis ofthese information, the chromosome is formed. For example, the sup-plier information will show about howmany suppliers are consideredand the engagement cost is also known for each supplier. The locationis also a very important information as the taxes or duties are decidedon the basis of location of the supplier. The information of theavailable transportation modes at each supplier with the cost isalso important, whereas the demand information is also importantto form a chromosome. The structure of chromosome is identicalas taken by Ding et al. [18]. The chromosome will be representedas in Fig. 6.

From Fig. 6, it is clear that first four variables are shown for suppli-er means if one is selected put 1 otherwise 0.Whereas next 8 variablesare for the weight allocated to the various transportation modes. Inthe last two columns, the reorder point and demand quantity forthe selected supplier is represented.

8.2. Evaluation

In this step, each sequence has been calculated according to theevaluation criteria, which is a problem specific function. In the real

world state of affairs, several objectives work at the same time.Thus, the proposed algorithm provides the facility to specify severalobjectives. The user can specify the relative weighted average foreach objective. In the proposed algorithm (KBGA), the knowledgebased system is highly efficient for sustaining the solution feasibility.In the present study, there are two objectives have taken into consid-eration. Those are total cost and demand fill rate. Both are conflictingin nature. Therefore a pareto front has been considered to satisfy bothobjectives.

8.3. Knowledge based selection (KBS)

After the evaluation of all the sequences, a subset of the initialpopulation is selected on random basis. It works on the basis of Dar-winism “Survival of the Fittest” but not as a greedy algorithm. InKBGA, the selection is also affected by the knowledge base systemto improve the performance of the algorithm.

In this algorithm, the selection is based on Neo Darwinism [26],which can sub-divide the procedure of selection of three categories:a) Directional selection, b) Steady selection and c) Unruly selection.The directional selection is based on the mean value (increasing ordecreasing both) of the population whereas steady selection, whichis based on normalizing, eliminates the chromosomes with excessivevalues. It is called steady selection due to provide the steady statesearch space. The chromosomes are eliminated according to the mod-erate values in unruly selection. To execute all three types of selec-tion, there are several methods of the selection e.g. tournamentselection, roulette wheel selection, logarithmic scales selection etc.

In the knowledge base system, all types of selection schemes withtheir characteristics and their performance in different systems havebeen placed. According to this knowledge, the suitable selectionscheme has been applied for the selection of a subset of the initialpopulation for the next stage of the algorithm.

8.4. Knowledge based crossover (KBC)

Following the KBS, the surviving chromosomes are selected toform the new off springs to explore the wider search space. Theknowledge based crossover gives the inherent characteristics to theoff springs from parents. Initially, a sub-set of survived chromosomeshas been randomly selected according to the crossover probability. Toperform the crossover, there are several crossover schemes e.g. singlepoint crossover, partial mapping crossover, uniform crossover, cyclecrossover etc. with some specific characteristics.

The characteristics of each crossover scheme and their perfor-mance for different types of system environments and problemshave been kept in the knowledge base and it will be updated as in-creasing the knowledge. The tuning of the crossover probability isalso a concern in the proposed algorithm. The performance of the sys-tem for the different environments at the various crossover probabil-ities has been captured and placed in the knowledge base. Anotherfacility to check the unfeasible new offspring has been providedto the user. If any parent reproduce an unfeasible solution thatwill be checked and discarded with the help of knowledge basesystem.

8.5. Knowledge based mutation

Following the above step, the next genetic operator, named as mu-tation, empowers the algorithm to explore the search space. It mod-ifies single chromosome by altering the genes or bits instead ofrecombining the two chromosomes. In the proposed algorithm, aknowledge base has been created to store the knowledge about theperformance of various mutation operators e.g. inversion, insertion,displacement etc. in the different system environments with a varietyof objective function. It also has the knowledge about the outcomes

Input (Information from all the sources)

Supplier Information

DemandInformation

TransportationInformation

LocationInformation Supply Chain

Information

Is information relevant for network

optimization?Close the case

Best Practiced Alternatives

Plan the work accordingto the performance

measure and requirements

Design or select the network (suppliers)

according to performance measures

Review the outcomes

Is there any other information required?

Knowledge Base Make the initial population of KBGA

No

Yes

No

Yes

Fig. 5. Initialization process of KBGA.

534 A. Prakash et al. / Decision Support Systems 52 (2012) 528–538

with the different ranges of the mutation probability. According toMichalewicz (1992), the selection of the appropriate value of the mu-tation probability is an art not a science. Hence, it is cleared now thatknowledge (explicit or implicit) can help to determine the value ofgenetic parameter (Fig. 9).

8.6. Termination criteria

After mutation, the selected populations, equal to the size of initialpopulation, have to be entered to the next generation out of the ex-tended population of the chromosomes. The whole process will be

Binary variablesfor supplier

Integer variables for weights allocate to transportation mode

Reorder quantity

Demandquantity

Fig. 6. Representation of chromosome.

repeated until satisfy the termination criteria. The termination cri-teria can be characterized by the number of generations or the prede-fined level of the output.

9. Numerical analysis

In the present study, a supply chain network optimization problemhas been addressed and due to much complexity it is solved by the im-proved version of genetic algorithm which is having the power ofknowledge also. This algorithm is known as knowledge based geneticalgorithm and it is employed for supply chain network optimization.As the real world problem, the demand is uncertain and it follows thenormal distribution. The main objective of the present study is the de-mand satisfaction or demand fill rate and unit cost; both of these objec-tives are conflicting in nature, therefore a pareto front has beenachieved which shows the various optimal point according to theweights. The engagement cost has been introduced the cost of contractnegotiation. For economies of scale, there is minimum order size hasbeen set out by each supplier. It is also assumed that the order hasbeen directly given to the suppliers. A supplier can refuse the orderif it is less than the minimum order size. Another novelty of thisstudy is that the penalty cost for the lost demand has also beenconsidered.

4 2 5 8 1 m

1 2 6 9 3 m

3 5 2 1 7 m

8 4 6 1 3 m

7 9 5 3 1 m

1

2

3

4

n

Knowledge Based

Selection

(KBS)

4 2 5 8 1 m

4 2 5 8 1 m

3 6 9 8 7 m

5 9 8 4 2 m

8 3 5 7 1 m

1

2

3

4

n

Initial Population Selected Population

Selection Schemes e.g .

roulette wheel, tournament etc.

Selection Criteria

Fig. 7. Knowledge based selection.

7 4863251

1 2368547

6 8425731

4 6217583

KnowledgeBased

Crossover(KBC)

1 2364758

7 4861532

4 6285731

6 8417523

CrossoverSchemes e.g.

PMX, CLX etc.

CrossoverProbability

Parents Chromosomes Offspring Chromosomes

Fig. 8. Knowledge based crossover.

535A. Prakash et al. / Decision Support Systems 52 (2012) 528–538

As the problem statement is identical as considered in Ding et al.[18]. Therefore the demand is 300 pairs of boots. Initially the penaltycost has not been considered and compared it with the resultsaddressed from Ding et al. [18]. The results obtained from SGA [18]have been shown in Fig. 10.

The results obtained from KBGA have been shown in Fig. 11, with-out considering the lost sales penalty. It shows the smoothness of thecurve and it delineates that after reaching beyond the 98.5% of fillrate, the unit price will almost be the same. Therefore, it will try toimprove the suppliers' service also.

4 6217583

KnowlBase

Mutat(KBM

MutatSchemeINS, IN

MutatProbab

Chromosomes

Fig. 9. Knowledge b

The efficacy of KBGA has been shown in the results. The conver-gence rate is also faster as in SGA it converges in 2000 generations[18] whereas in KBGA it converges only in 144 generations.

The results are also obtained for with lost sales penalty and shownin Fig. 12. The figure shows that after considering the lost sales penal-ty the unit price is comparatively very high and in this case it will bevery near to real world situation.

Several important solutions have been summarized in Table 3.From the table, it can be said that the results can be classified intwo categories: solutions up to the demand fill rate 95.8% select the

edge d ion

)

6 8517423

ion s e.g. V etc.

ionility

Mutated Chromosomes

ased mutation.

2 33 32 32 3 428

9

9

8

10

Fig. 10. Results obtained from SGA.Adopted from Ding et al. 2006.

Fig. 12. Pareto front obtained from KBGA with lost sales penalty (d=300).

Table 3Various pareto solutions (d=300).

E1 E2 Supplierportfolio

Transportation allocationweights (%)

Reorderpoint

Orderquantity

38.26 100 S2+S3 L2 (14+25+33)+L3(28) 6273 158738.14 99.99 S2+S3 L2 (17+19+36)+L3(28) 6142 156236.42 97.5 S2+S3 L2 (28+15+29)+L3(28) 6085 155035.37 95.8 S2+S3 L2 (32+12+28)+L3(28) 5322 150730.44 90.5 S2 L2 (38+23+49) 5536 118527.08 87.5 S2 L2 (38+21+41) 5283 111021.92 82.0 S2 L2 (42+19+38) 4892 100519.75 80.0 S2 L2 (46+19+35) 5227 1005

536 A. Prakash et al. / Decision Support Systems 52 (2012) 528–538

same supplier portfolio i.e. S2 and S3 whereas solutions below de-mand fill rate 95% there is need of only one supplier S2. The studyshows that the supplier S2 is an efficient supplier. Whereas, SGAsearch the results only up to 97.2% of demand fill rate with multiplesuppliers. The reorder point is also lower in the solution achievedby KBGA. The order quantity is also lower than results suggested bySGA. Therefore, it affects the inventory cost of the supply chain andmakes an effort to mitigate the effect of high inventory and makethe lean supply chain also. On the other hand, it is clear that as the de-mand fill rate decreases, the reorder point is decreased and orderquantity is increased. It also lessens the inventory but lost the sale si-multaneously. Therefore, the lesser inventory is not always justifiedas it is also the cause of lost sale and it increases the cost as the pen-alty of lost sales. From the table, it can be concluded that multiplesuppliers are beneficial for more demand fill rate as unique supplieris beneficial only below 95.8% of demand fill. The justifications ofthe advantages of selecting the multiple suppliers are also shownfrom the other results also in Table 3.

To show the efficiency to handle the complex problem, the KBGAhas also been tested on the more complex problems i.e. with increas-ing demand. It has also tested on demand of 400 and 500. Theobtained pareto fronts have been shown in Fig. 13. The convergencerate is also very fast. The algorithm has been converged only in 178generations for demand of 400. For demand of 500, KBGA has beenconverged in 243 generations which shows the faster convergencerate.

From the above shown results, it can be scrutinized that the pro-posed algorithm (KBGA) is an efficient algorithm for tackling thecomplex problems of supply chain. The power of knowledge hasalso been shown from the results on comparing with SGA. Thestudy shows that KBGA provides the solution in less generation i.e.less time than SGA. The present study is enhanced the theoretical ap-proach to solve such complex problem and numerical analysis showsthat it can be worked for real supply chain problems with someamendments. The study is much intended to show the efficacy ofKBGA and the numerical results strengthen the above concept.

Fig. 11. Pareto front obtained from KBGA without lost sales penalty (d=300).

The proposed heuristic KBGA has been coded in C++ program-ming language and the experiment has been carried out on an IBMPC with a Pentium IV CPU −1.9 GHz processor. To sum up, for allthe aforementioned results not only authenticate the supremacy ofthe proposed algorithm over existing heuristic but provide also anew dimension to the solution of complex combinatorial problemsin real time.

10. Conclusion

The present paper provides a new insight to the practitioner tosolve the different combinatorial problems e.g. network optimizationin the supply chain context. The network optimization in the flexiblesupply chain context is a very complex problem for the practitioners.Because the dynamics of a system comprising a huge number of moreor less independently acting self-controlled entities within a networkis hard to predict and evaluate in real operation, appropriate algo-rithm is required for this purpose. The proposed algorithm, KBGA, im-proves the performance of traditional GA through introducing theknowledge base system which includes both explicit and implicitknowledge. Therefore, the most significant contribution of this re-search is to develop new algorithm which is known as KnowledgeBased Genetic Algorithm (KBGA) for improving the performance ofsupply chain. The proposed algorithm, KBGA, improves the perfor-mance of traditional GA through introducing the knowledge base sys-tem which includes both explicit and implicit knowledge. It mainlyemphasizes on the initialization, selection and genetic operators.The effectiveness of the productivity of classical meta-heuristics

Fig. 13. Pareto front obtained from KBGA with lost sales penalty (d=400 and 500).

537A. Prakash et al. / Decision Support Systems 52 (2012) 528–538

based on knowledge rather than information is intended towards cre-ating worthy knowledge and giving sufficient privileges to the same.This research can also be exploited to other multi objective problemswith more flexible attributes. In the new economy brought about byglobalization, the fast changing nature of the technology warrantsconsideration for the formation of knowledge integration with suchmeta-heuristics. To show the efficacy of the proposed KBGA, a com-parative study has also been made with SGA. This study shows thefaster convergence rate of KBGA with better quality solution. Aknowledge-based view of the algorithm is necessary to understandthe requirement of the real world attributes and vis-à-vis the algo-rithm capability.

This research has enlightened the domain of supply chain networkoptimization as it discusses about the commitment of faster deliveryat minimum cost. The mangers can apply the solutions with providingmore constraints accordance with the environment of the market andsupply chain. The network optimization problem can also give a newvision to the managers of supply chain to achieve the solution in sucha way that can fulfill the demand of the customer with minimum av-erage cost per product. Therefore, it will provide a two dimensionalapproach at the same time. However, the conclusion that while par-ticular improvement initiatives is beneficial towards certain perfor-mance dimension; it may negatively affect other performancemeasure underlines caution to the managers to be careful in selectingthe improvement initiatives. This research provides a new insightabout the optimization algorithms in theoretical manner but it canbe employed in real industry problems also with some new con-straints and the numerical analysis proved the same concept.

As a future scope, this research can be stretched out to variousproblems of the supply chain environment that cover the balancingor allocation of resources. This research can also be employed forthe multi-criterion decision making problems in FMS environmentas well as flexible supply chain environment.

Acknowledgments

The work described in this paper was substantially supported by agrant from the Research Grants Council of the Hong Kong Special Ad-ministrative Region, China (ProjectNo. PolyU510410). The authors alsothank the editor and the reviewers for their valuable comments andsuggestions that have led to the substantial improvement of the paper.

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538 A. Prakash et al. / Decision Support Systems 52 (2012) 528–538

Dr. Anuj Prakash is a young researcher who has done his

Ph.D. from IIT Delhi. He is working in the domain of FMS,CIM, supply chain management, Operation Management,Optimization. His research involves GA, SA, AIS, and FuzzySystems applications to the flexible system problems. Hehas some good publications in some internationals jour-nals and conferences.

th

Dr. Felix T. S. Chan received his BSc Degree in MechanicalEngineering from Brighton Polytechnic (now University),UK, and obtained his MSc and PhD in ManufacturingEngineering from the Imperial College of Science andTechnology, University of London, UK. Dr Chan is now anAssociate Professor in the Department of Industrial andSystems Engineering, The Hong Kong Polytechnic Univer-sity. His current research interests are Logistics and SupplyChain Management, Distribution Coordination, SystemsModelling and Simulation, Supplier Selection. To date, hehas published nine book chapters, over 200 refereed inter-national journal papers and 200 peer reviewed interna-tional conference papers. He is a Chartered Member of

e Chartered Institute of Logistics and Transport in Hong Kong.

Dr. Haitao Liao is an Assistant Professor in Department of Industrial & InformationEngineering and Nuclear Engineering Department at the University of Tennessee,Knoxville. He received his Ph.D. degree from the Department of Industrial and SystemsEngineering at Rutgers University. He also received M.S. degrees in Industrial Engineer-ing and Statistics, both from Rutgers University. His research interests focus on Model-ing of Accelerated Testing, Probabilistic Risk Assessment, Maintenance Models andOptimization, Spare Part Inventory Control, and Prognostics. His current research issponsored by National Science Foundation and U.S. Nuclear Regulatory Commission.He is a member of IIE and INFORMS. He is a recipient of National Science FoundationCAREER Award in 2010 and the 2010 William A.J. Golomski Award.

Prof. S.G. Deshmukh is a Professor in the Mechanical Engi-neering Department at Indian Institute of Technology (IIT),Delhi. His papers have been published in many reputable in-ternational journals like International Journal of Operations &ProductionManagement, International Journal of Productivi-ty and Performance Management, Production Planning andControl, International Journal of Production Research, etc.